Subgroups — C₂×C₈₉×#2567 #36412788

Order 22784.

2790 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2567	C₂	1	16	yes	maximal, direct product factor
4	C₂×#395×C₈₉	C₂	1	4	yes	maximal
5	C₂×#391×C₈₉	C₂	1	2	yes	maximal
6	C₂×#389×C₈₉	C₂	1	4	yes	maximal
7	C₂×#384×C₈₉	C₂	1	2	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₈₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₈₉	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	8	yes	—
13	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
14	C₂×C₄×Q₈×C₈₉	C₂²	1	8	yes	—
15	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₈₉	C₂²	1	8	yes	—
20	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
22	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
24	#395×C₈₉	C₂²	1	32	yes	—
25	#391×C₈₉	C₂²	1	16	yes	—
26	#389×C₈₉	C₂²	1	32	yes	—
27	#384×C₈₉	C₂²	1	16	yes	—
28	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	—
29	C₂×#95×C₈₉	C₂²	1	8	yes	—
30	C₂×#95×C₈₉	C₂²	1	2	yes	—
31	C₂²×Q₈×C₈₉	—	2	4	no	—
32	C₂²×Q₈×C₈₉	—	2	8	no	—
33	C₂²×Q₈×C₈₉	—	2	4	no	—
34	C₂²×Q₈×C₈₉	—	4	8	no	—
35	C₂²×Q₈×C₈₉	Q₈	1	8	yes	complemented
36	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
37	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
38	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
39	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
45	C₄⋊Q₈×C₈₉	—	2	32	no	—
46	C₄×Q₈×C₈₉	—	2	32	no	—
47	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
50	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
51	C₂×C₄⋊C₄×C₈₉	—	4	16	no	—
52	C₂×C₄⋊C₄×C₈₉	Q₈	1	16	yes	complemented
53	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
55	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₈₉	C₂³	1	32	yes	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
59	C₂×C₄²×C₈₉	—	2	8	no	—
60	C₂×C₄²×C₈₉	—	2	8	no	—
61	C₂×C₄²×C₈₉	D₄	1	8	yes	—
62	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
63	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
64	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
65	#95×C₈₉	C₂³	1	8	yes	—
66	#95×C₈₉	C₂³	1	32	yes	—
67	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
68	C₂×Q₈×C₈₉	—	2	32	no	—
69	C₂×Q₈×C₈₉	—	2	8	no	—
70	C₂×Q₈×C₈₉	—	2	16	no	—
71	C₂×Q₈×C₈₉	—	2	8	no	—
72	C₂×Q₈×C₈₉	—	4	16	no	—
73	C₂×Q₈×C₈₉	—	4	32	no	—
74	C₂×Q₈×C₈₉	C₂×Q₈	1	16	yes	complemented
75	C₂²×C₄×C₈₉	—	2	4	no	—
76	C₂²×C₄×C₈₉	—	2	8	no	—
77	C₂²×C₄×C₈₉	—	2	4	no	—
78	C₂²×C₄×C₈₉	—	2	8	no	—
79	C₂²×C₄×C₈₉	—	2	4	no	—
80	C₂²×C₄×C₈₉	—	2	4	no	—
81	C₂²×C₄×C₈₉	—	2	8	no	—
82	C₂²×C₄×C₈₉	—	2	8	no	—
83	C₂²×C₄×C₈₉	—	2	16	no	—
84	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
85	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₈₉	C₂×Q₈	1	16	yes	—
88	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
89	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
90	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
91	C₂²×C₄×C₈₉	#41	1	4	yes	—
92	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
93	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
97	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
99	C₄⋊C₄×C₈₉	—	2	16	no	—
100	C₄⋊C₄×C₈₉	—	2	8	no	—
101	C₄⋊C₄×C₈₉	—	2	16	no	—
102	C₄⋊C₄×C₈₉	—	2	16	no	—
103	C₄⋊C₄×C₈₉	—	4	32	no	—
104	C₄⋊C₄×C₈₉	C₂×Q₈	1	32	yes	complemented
105	C₄²×C₈₉	—	2	16	no	—
106	C₄²×C₈₉	—	2	16	no	—
107	C₄²×C₈₉	C₂×D₄	1	16	yes	—
108	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
109	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
110	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
111	C₂³×C₈₉	C₂×#41	1	2	yes	—
112	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
113	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
114	Q₈×C₈₉	—	2	32	no	—
115	Q₈×C₈₉	—	4	32	no	—
116	C₂×C₄×C₈₉	—	2	16	no	—
117	C₂×C₄×C₈₉	—	2	8	no	—
118	C₂×C₄×C₈₉	—	2	32	no	—
119	C₂×C₄×C₈₉	—	2	4	no	—
120	C₂×C₄×C₈₉	—	2	8	no	—
121	C₂×C₄×C₈₉	—	2	4	no	—
122	C₂×C₄×C₈₉	—	2	8	no	—
123	C₂×C₄×C₈₉	—	2	4	no	—
124	C₂×C₄×C₈₉	—	2	4	no	—
125	C₂×C₄×C₈₉	—	2	8	no	—
126	C₂×C₄×C₈₉	—	2	8	no	—
127	C₂×C₄×C₈₉	—	2	16	no	—
128	C₂×C₄×C₈₉	—	4	8	no	—
129	C₂×C₄×C₈₉	—	4	16	no	—
130	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	—
131	C₂×C₄×C₈₉	C₄⋊Q₈	1	16	yes	—
132	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
133	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
134	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
135	C₂×C₄×C₈₉	C₂²×Q₈	1	16	yes	—
136	C₂×C₄×C₈₉	C₂²×Q₈	1	8	yes	—
137	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
138	C₂×C₄×C₈₉	C₂²×Q₈	1	8	yes	—
139	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
140	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
141	C₂²×C₈₉	C₂×C₄⋊Q₈	1	4	yes	—
142	C₂²×C₈₉	#535	1	4	yes	—
143	C₂²×C₈₉	#554	1	8	yes	—
144	C₂²×C₈₉	Q₈²	1	8	yes	—
145	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
146	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
147	C₂²×C₈₉	C₂³×Q₈	1	2	yes	—
148	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
149	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
150	C₄×C₈₉	—	2	8	no	—
151	C₄×C₈₉	—	2	4	no	—
152	C₄×C₈₉	—	2	16	no	—
153	C₄×C₈₉	—	4	4	no	—
154	C₄×C₈₉	—	4	8	no	—
155	C₄×C₈₉	C₂×C₂²⋊Q₈	1	8	yes	—
156	C₄×C₈₉	C₂×C₄⋊Q₈	1	8	yes	—
157	C₂×#2567	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂×C₈₉	#2567	1	8	yes	direct product factor
159	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₈₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
161	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
162	C₂×C₈₉	C₂×#554	1	2	yes	—
163	C₂×C₈₉	C₂×Q₈²	1	2	yes	—
164	C₂²×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
165	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
166	#2567	C₂×C₈₉	1	16	yes	direct product factor
167	C₂×#395	C₂×C₈₉	1	4	yes	—
168	C₂×#391	C₂×C₈₉	1	2	yes	—
169	C₂×#389	C₂×C₈₉	1	4	yes	—
170	C₂×#384	C₂×C₈₉	1	2	yes	—
171	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic
172	C₈₉	C₂×#2567	1	1	yes	characteristic, direct product factor, Sylow
173	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
174	C₂³×Q₈	C₂²×C₈₉	1	2	yes	—
175	C₂×C₄⋊Q₈	—	2	8	no	—
176	C₂×C₄⋊Q₈	C₂²×C₈₉	1	8	yes	—
177	C₂×C₄×Q₈	—	2	8	no	—
178	C₂×C₄×Q₈	C₂²×C₈₉	1	8	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₈₉	1	8	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
185	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
186	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
187	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
188	#395	C₂²×C₈₉	1	32	yes	—
189	#391	C₂²×C₈₉	1	16	yes	—
190	#389	C₂²×C₈₉	1	32	yes	—
191	#384	C₂²×C₈₉	1	16	yes	—
192	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	—
193	C₂×#95	C₂²×C₈₉	1	2	yes	—
194	C₂×#95	C₂²×C₈₉	1	8	yes	—
195	C₂²×Q₈	—	2	4	no	—
196	C₂²×Q₈	—	2	8	no	—
197	C₂²×Q₈	—	2	4	no	—
198	C₂²×Q₈	—	4	8	no	—
199	C₂²×Q₈	Q₈×C₈₉	1	8	yes	complemented
200	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
201	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
202	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
203	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
204	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
205	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
206	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
207	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
209	C₄⋊Q₈	—	2	32	no	—
210	C₄×Q₈	—	2	32	no	—
211	C₂×C₄⋊C₄	—	2	8	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	8	no	—
214	C₂×C₄⋊C₄	—	2	8	no	—
215	C₂×C₄⋊C₄	—	4	16	no	—
216	C₂×C₄⋊C₄	Q₈×C₈₉	1	16	yes	complemented
217	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
218	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
219	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
220	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
221	C₂×C₄⋊C₄	C₂³×C₈₉	1	32	yes	—
222	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
223	C₂×C₄²	—	2	8	no	—
224	C₂×C₄²	—	2	8	no	—
225	C₂×C₄²	D₄×C₈₉	1	8	yes	—
226	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
227	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
228	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
229	#95	C₂³×C₈₉	1	8	yes	—
230	#95	C₂³×C₈₉	1	32	yes	—
231	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
232	C₂×Q₈	—	2	32	no	—
233	C₂×Q₈	—	2	8	no	—
234	C₂×Q₈	—	2	16	no	—
235	C₂×Q₈	—	2	8	no	—
236	C₂×Q₈	—	4	16	no	—
237	C₂×Q₈	—	4	32	no	—
238	C₂×Q₈	C₂×Q₈×C₈₉	1	16	yes	complemented
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	8	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	16	no	—
248	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
249	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
250	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
251	C₂²×C₄	C₂×Q₈×C₈₉	1	16	yes	—
252	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
253	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
254	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
255	C₂²×C₄	#41×C₈₉	1	4	yes	—
256	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
257	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
258	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
259	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
260	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
261	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
262	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
263	C₄⋊C₄	—	2	16	no	—
264	C₄⋊C₄	—	2	8	no	—
265	C₄⋊C₄	—	2	16	no	—
266	C₄⋊C₄	—	2	16	no	—
267	C₄⋊C₄	—	4	32	no	—
268	C₄⋊C₄	C₂×Q₈×C₈₉	1	32	yes	complemented
269	C₄²	—	2	16	no	—
270	C₄²	—	2	16	no	—
271	C₄²	C₂×D₄×C₈₉	1	16	yes	—
272	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
273	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
274	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
275	C₂³	C₂×#41×C₈₉	1	2	yes	—
276	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
277	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
278	Q₈	—	2	32	no	—
279	Q₈	—	4	32	no	—
280	C₂×C₄	—	2	16	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	32	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	16	no	—
292	C₂×C₄	—	4	8	no	—
293	C₂×C₄	—	4	16	no	—
294	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	—
295	C₂×C₄	C₄⋊Q₈×C₈₉	1	16	yes	—
296	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
297	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
298	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
299	C₂×C₄	C₂²×Q₈×C₈₉	1	16	yes	—
300	C₂×C₄	C₂²×Q₈×C₈₉	1	8	yes	—
301	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
302	C₂×C₄	C₂²×Q₈×C₈₉	1	8	yes	—
303	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
304	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
305	C₂²	C₂×C₄⋊Q₈×C₈₉	1	4	yes	—
306	C₂²	#535×C₈₉	1	4	yes	—
307	C₂²	#554×C₈₉	1	8	yes	—
308	C₂²	Q₈²×C₈₉	1	8	yes	—
309	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
310	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
311	C₂²	C₂³×Q₈×C₈₉	1	2	yes	—
312	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
313	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
314	C₄	—	2	8	no	—
315	C₄	—	2	4	no	—
316	C₄	—	2	16	no	—
317	C₄	—	4	8	no	—
318	C₄	—	4	4	no	—
319	C₄	C₂×C₂²⋊Q₈×C₈₉	1	8	yes	—
320	C₄	C₂×C₄⋊Q₈×C₈₉	1	8	yes	—
321	C₂	C₈₉×#2567	1	8	yes	direct product factor
322	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
323	C₂	C₂²×C₄⋊Q₈×C₈₉	1	1	yes	characteristic
324	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
325	C₂	C₂×#554×C₈₉	1	2	yes	—
326	C₂	C₂×Q₈²×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₈₉×#2567	C₂	direct (N × H)
35. C₂²×Q₈×C₈₉	Q₈	semidirect
52. C₂×C₄⋊C₄×C₈₉	Q₈	semidirect
74. C₂×Q₈×C₈₉	C₂×Q₈	semidirect
104. C₄⋊C₄×C₈₉	C₂×Q₈	semidirect
157. C₂×#2567	C₈₉	direct (N × H)
158. C₂×C₈₉	#2567	direct (N × H)
166. #2567	C₂×C₈₉	direct (N × H)
172. C₈₉	C₂×#2567	direct (N × H)
199. C₂²×Q₈	Q₈×C₈₉	semidirect
216. C₂×C₄⋊C₄	Q₈×C₈₉	semidirect
238. C₂×Q₈	C₂×Q₈×C₈₉	semidirect
268. C₄⋊C₄	C₂×Q₈×C₈₉	semidirect
321. C₂	C₈₉×#2567	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄⋊Q₈×C₈₉	2
C₂²×C₄×Q₈×C₈₉	2
C₈₉×#2567	2
C₂×#395×C₈₉	2
C₂×#391×C₈₉	2
C₂×#389×C₈₉	2
C₂×#384×C₈₉	2
C₂×C₄×C₄⋊C₄×C₈₉	2
C₂×#2567	89

Subgroups — C2×C89×#2567 #36412788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2567 #36412788